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Journal of the Optical Society of America B

Stochastic quantum interferometry with Fock states

F. De Martini, Paolo Mataloni, Giovanni Di Giuseppe, Fabrizio Altarelli

Published May 1, 2002• 2 citations
Publisher

Abstract

We report the experimental realization of first- and second-order optical stochastic interferometry with single-photon Fock states and with a couple of photons generated by spontaneous parametric downconversion. The behavior of the constitutive element of the stochastic interferometer, the stochastic beam splitter, is theoretically described, both for first- and second-order interferometry. The theory predicts a reduction of the visibility from 1 to π/4 and to 1/2, respectively, for the two cases. These results are a direct consequence of the presence of Bose–Einstein correlations within the electromagnetic field. The visibility reduction obtained in the two experiments and their comparison with theoretical predictions are discussed in detail.

DOI
10.1364/josab.19.001009

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We report the experimental realization of first- and second-order optical stochastic interferometry with single-photon Fock states and with a couple of photons generated by spontaneous parametric downconversion. The behavior of the constitutive element of the stochastic interferometer, the stochastic beam splitter, is theoretically described, both for first- and second-order interferometry. The theory predicts a reduction of the visibility from 1 to π/4 and to 1/2, respectively, for the two cases. These results are a direct consequence of the presence of Bose–Einstein correlations within the electromagnetic field. The visibility reduction obtained in the two experiments and their comparison with theoretical predictions are discussed in detail.
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After a very brief review of the historical Einstein, Podolsky, and Rosen (EPR) experiments, a new two-photon interference type EPR experiment is reported. A two-photon state was generated by optical parametric down conversion. Pairs of light quanta with degenerate frequency but divergent directions of propagation were sent to two independent Michelson interferometers. First and second order interference effectors were studied. Different than other reports, we observed that the second order interference visibility vanished when the optical path difference of the interferometers were much less than the coherence length of the pumping laser beam. However, we also observed that the second order interference behaved differently depending on whether the interferometers were set at equal or different optical path differences.
Quantum mechanical models of beam splitters1 predict interesting fourth-order interference effects when nonclassical light is used. If indistinguishable one-photon states are simultaneously input into each port of a 50/50 beam splitter, the theory predicts that each output will contain either two photons or none. A naive (particle) theory would predict a mixture of two’s and one’s. The required |1,1〉 photon state can be selected in nondegenerate parametric downconversion experiments by photon-counting coincidence detection. The disappearance of this coincidence after a beam splitter has recently been studied,1-2 and the range of path length differences over which the effect can be seen is related by Fourier transform to the photon bandwidth. In our work the bandwidth is not limited by external filters, and we have developed a theory which relates the measured photon length to the geometry of the apparatus and the detailed phase matching conditions at the parametric crystal. This theory of phase matching viewed through a beam splitter produces some unexpected results when the beam splitter is tilted and when large aperture detectors are considered.
Fourth-order interference patterns of biphotons generated by type-I spontaneous parametric downconversion are examined for beams with partial angular and spectral entanglement, both for degenerate and nondegenerate constituent photons. Two-beam configurations using a single beam-splitter interferometer and a Mach-Zehnder interferometer are explicitly studied, as are four-beam configurations using pairs of beam splitters and Mach-Zehnder interferometers. The interference pattern generally comprises a number of harmonic functions of the path-length difference with frequencies and visibilities that usually depend on direction, and may have a finite or infinite duration (fourth-order coherence length). The relation between the visibility and the spectral indistinguishability of the two beams is established. Certain components of the interference pattern are independent of direction so that they are not washed out by the use of apertures of finite size.
Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in type-2 spontaneous parametric down-conversion is demonstrated by the observation of quantum interference with 98% visibility in a simple beam-splitter (Hanburry Brown-Twiss) anticorrelation experiment. The nonlocal cancellation of two-photon probability amplitudes as a result of this double entanglement allows us to demonstrate two different types of Bell's inequality violations in one experimental setup.